I'm desperate to see EditPlus alternative on Linux, as I cannot live with anything else that this peculiar editor :L
I am not a Linux user, but it would seem to me the first thing to do is to try EditPlus on Wine
If you can't get that to work, or you find the performance unsatisfactory, you could try gedit (for GNOME) or KATE (for KDE). These seem to be among the favorites on Linux. I have recently tried Geany (multiplatform), and it seems promising. Depending on what you specifically like about EditPlus, these alternatives could be just as good, or they could be much, much worse.
But the fact that there is a page on the EditPlus wiki devoted to running it on Linux suggests that this is possible. If you have trouble, try asking the EditPlus community for tips. There is a support page on the EditPlus main site with links to various resources.